OFFSET
1,2
COMMENTS
Comment from Sean A. Irvine, edited by Natan Arie Consigli, Dec 26 2016 : (Start)
This is the counting series for the hypothetical stereo-isomers of all acyclic hydrocarbons that satisfy the octet rule.
A036673 is the variant with triple bonds excluded.
A002986 doesn't count stereoisomers.
The reference gives a three-variable generating function and cycle-index over A4 which can produce both these sequences. There are also dependencies on earlier generating functions.
(End)
Read has incorrect a(10)=27100. - Sean A. Irvine, Nov 20 2020
LINKS
Sean A. Irvine, Correction of A036672(10) and A036673(10), 2020
Sean A. Irvine, Java program (github)
R. C. Read, The Enumeration of Acyclic Chemical Compounds, pp. 25-61 of A. T. Balaban, ed., Chemical Applications of Graph Theory, Ac. Press, 1976. [Annotated scanned copy] See p. 60.
Wikipedia, Stereoisomerism
EXAMPLE
From M. F. Hasler, Dec 26 2016: (Start)
For n = 1, there is only a(1) = 1 possibility, CH4.
For n = 2, one has C2H6 (ethane, H3C-CH3), C2H4 (ethylene, H2C=CH2 with a double bond), C2H2 (ethyne, HC≡CH, triple bond), whence a(2) = 3.
For n = 3, one has C3H8 (H3C-CH2-CH3), C3H6 (H2C=CH-CH3, propene), and two C3H4 (H2C=C=CH2, propadiene, and HC≡C-CH3: methylacetylene), thus a(3) = 4. Cyclic molecules like cyclopropane C3H6 and cyclopropropene C3H4 are excluded. (End)
From Natan Arie Consigli, Dec 26 2016: (Start)
For n = 4, we have butane, isobutane, 1-butene, cis/trans-2-butene, buta-1,2-diene, buta-1,3-diene, butatriene, isobutylene, but-1-yne, but-2-yne, diacetylene, but-1-en-3-yne.
For n = 5 we have:
- 3 alkanes: pentane, methylbutane and neopentane.
- 17 alkenes: 1-pentene, (E/Z)-2-pentene, 1,2-pentadiene, (E/Z)-1,3-pentadiene, 1,4-pentadiene, 1,2,3-petatriene, penta-1,2,4-triene, pentatetraene, 2-methylbut-1-ene, 2-methylbut-2-ene, 3-methylbut-1-ene, isoprene, 3-methylbuta-1,2-diene, (R/S)-penta-2,3-diene.
-11 alkynes: 1-pentyne, 2-pentyne, pent-1-en-4-yne, (E/Z)-pent-3-en-1-yne, penta-1,2-dien-4-yne, penta-1,4-diyne, penta-1,3-diyne, pent-1-en-3-yne, 3-methylbut-1-yne, 2-methylbut-1-en-3-yne. (End)
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
a(10) corrected and more terms from Sean A. Irvine, Nov 20 2020
STATUS
approved